Edge computing nodes undertake an increasing number of tasks with the rise of business density. Therefore, how to efficiently allocate large-scale and dynamic workloads to edge computing resources has become a critical challenge. This study proposes an edge task scheduling approach based on an improved Double Deep Q Network (DQN), which is adopted to separate the calculations of target Q values and the selection of the action in two networks. A new reward function is designed, and a control unit is added to the experience replay unit of the agent. The management of experience data are also modified to fully utilize its value and improve learning efficiency. Reinforcement learning agents usually learn from an ignorant state, which is inefficient. As such, this study proposes a novel particle swarm optimization algorithm with an improved fitness function, which can generate optimal solutions for task scheduling. These optimized solutions are provided for the agent to pre-train network parameters to obtain a better cognition level. The proposed algorithm is compared with six other methods in simulation experiments. Results show that the proposed algorithm outperforms other benchmark methods regarding makespan.